Problem: What is the missing constant term in the perfect square that starts with $x^2-4x$ ?
Answer: Let $b$ be the missing constant term. Let's assume $x^2-4x+b$ is factored as the perfect square $(x+a)^2$. $\begin{aligned} (x+a)^2&=x^2+{2a}x+{a^2} \\\\ &=x^2{-4}x+ b \end{aligned}$ For the expressions to be the same, ${2a}$ must be equal to ${-4}$, and ${a^2}$ must be equal to $ b$. From ${2a=-4}$ we know that $a=-2$. Now, from ${a^2=b}$ we know that $b=(-2)^2=4$. Indeed, $x^2-4x+4$ is factored as $(x-2)^2$. In conclusion, the missing constant term in the perfect square that starts with $x^2-4x$ is $4$